A154250 a(n) = ( (9 + sqrt(7))^n - (9 - sqrt(7))^n )/(2*sqrt(7)).

1, 18, 250, 3168, 38524, 459000, 5411224, 63436032, 741418000, 8651257632, 100857705376, 1175245632000, 13690951178176, 159468944439168, 1857310612720000, 21630889140461568, 251915019187028224

Offset: 1

Author

Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009

Keywords

• nonn

Comments

lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(7) = 11.6457513110....

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..938
• Index entries for linear recurrences with constant coefficients, signature (18,-74).

Crossrefs

Cf. A010465 (decimal expansion of square root of 7).

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-7); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009

Mathematica

Join[{a=1,b=18},Table[c=18*b-74*a;a=b;b=c,{n,40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
LinearRecurrence[{18,-74},{1,18},20] (* Harvey P. Dale, Feb 16 2014 *)

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 18*a(n-1) - 74*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 18*x + 74*x^2). (End)

Extensions

Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009

Edited by Klaus Brockhaus, Oct 06 2009